A novel numerical method for multi-objective differentiable optimization, the Multiple-Gradient Descent Algorithmm (MGDA), has been proposed in [8] [11] to identify Pareto fronts. In MGDA, a direction of search for which the directional gradients of the objective functions are all negative, and often equal by construction [12], is identified and used in a steepest-descent-type iteration. The method converges to Pareto-optimal points. MGDA is here briefly reviewed to outline its principal theoretical properties and applied first to a classical mathematical test-case for illustration. The method is then ex-tended encompass cases where the functional gradients are approximated via meta-models, as it is often the case in complex situations, and demonstrated on three optimum-shape design problems in compressible aerodynamics.The first problem is purely related to aerodynamic performance. It is a wing shape optimization exercise w.r.t. lift and drag in typical transonic cruise